A phase-field fluid modeling and computation with interfacial profile correction term

We present a new phase-field fluid model and computation with minimized Cahn-Hilliard (CH) dynamics. Using the CH equation, the internal structure of the interface layer is determined by explicit smoothing flow discontinuities. This method greatly simplifies gridding, discretization, and handling of topological changes. The original CH equation, however, has intrinsic dynamics such as interface length minimization, i.e., the motion by minus the Laplacian of the mean curvature. When the CH equation is applied to the modeling of multiphase fluid flows, we want to minimize its interface length minimization property. The surface tension formulation also requires the multiphase fluid interface to be a hyperbolic tangent profile. Typically, under the advection of flow, the interfacial transition is not a hyperbolic tangent profile, i.e., it is too compressed or sharpened. Even though the original CH dynamics conserves the total mass, the enclosed area obtained by its interface is not preserved. To overcome these shortcomings, we propose a modified CH equation with an interfacial profile correction term. Several numerical examples are presented to show the accuracy of the proposed method. The numerical results demonstrate that the proposed modified CH equation preserves the enclosed area better than the original CH equation.